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Course: Content items for courses > Unit 13

Lesson 4: Integrating multivariable functions
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Multivariable calculus - staging
Integrating multivariable functions
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[OLD] Flux with surface integrals examples

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Example 1

Let f(x,y,z)=xı^+yȷ^+zk^. Find the flux of the vector field f through the curved part S of the cylinder with radius 3 and height 4.
S={(x,y,z)∈R3|x2+y2=32 and 0<z<4}

Step 1: Parameterize

Before we can find the flux through a surface, we need to parameterize it. A good first step whenever we try to parameterize a surface is to pick what coordinate system we want to use.
What is a good coordinate system for this problem?
Choose 1 answer:
Based on your answer, find a parameterization T for the surface S.

Step 2: Find the normal vector

The next step to solving for the flux through S is to find the normal vector that encodes the magnification information of the parameterization T.
What is the normal vector n→ to your parameterization for S?
Choose 1 answer:

Step 3: Integrate

Now that we have all the components to find the flux through S, all that's left is to solve the integral.
What is the flux of the vector field f through the curved surface S?
Choose 1 answer:

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